Sum and scalar product of fuzzy subhyperspaces

Abstract

The aim of this paper is to study the properties of two operations, sum and scalar product, on fuzzy subsets of hypervector spaces. In this regards, some new equivalent conditions of fuzzy subhyperspaces are introduced based on these operations. Also, the behavior of sum and scalar product of fuzzy subhyperspaces under linear transformations are investigated.

Subject Classification: (2010):

• 08A72
• 20N20

Keywords:

• Hyperoperation
• Hypervector space
• Fuzzy subset
• Fuzzy subhyperspace
• Linear transformation